Hi, I search for an example of a Sasakimanifold which is not Einstein. Can you give one?
Thank you and best regards!
Hi, I search for an example of a Sasakimanifold which is not Einstein. Can you give one? Thank you and best regards! 


Chapter 11 in BoyerGalicki's Sasakian Geometry discusses two obstructions to the existence of SasakiEinstein structures on Sasakian manifolds. They go on to discuss many such examples, obtained as links of conical singularities of projective varieties in weighted projective spaces. They are not hard to find! The cone of a Sasakian manifold is Kähler, whereas the cone of a SasakiEinstein manifold is CalabiYau. Hence your question is the analogue of asking for a Kähler manifold which is not CalabiYau. This is the generic situation. As in my answer to your first question on Sasakian Geometry, there is no excuse for these questions given the wealth of information and the clarity of style of the book by Boyer and Galicki. Go read the book! It really is good. 


This is not an answer to your question, but rather an extension of José FigueroaO'Farrill's answer. Roughly a year ago, a quick Google search led me to a preprint of Boyer & Galicki's wonderful book; it can be found here 


I am not very sure of everything here but I wonder if the example given in Appendix A on Page 21 of this paper by one of my professors meets your criteria. 

